Short

Term Load Forecasting:
Similar Day

Based Wavelet Neural
Networks
Ying Chen, Peter B.
Luh
,
Fellow, IEEE,
Che
Guan,
Yige
Zhao
Laurent D. Michel
Matthew A.
Coolbeth
,
Peter B.
Friedland
Stephen J.
Rourke
,
Senior Member, IEEE
World Congress on Intelligent Control and Automation, July 2008
IEEE TRANSACTIONS ON POWER SYSTEMS, Feb 2010
Outline
Background
Similar Day

Based Wavelet Neural Networks
Weekday Index and Weather
Similar Day

Based Load Input Selection
Decomposition Input Load
Neural Networks
Testing Results
Conclusion
Background
In deregulated electricity markets, short

term load
forecasting is important for reliable power system
operation, and significantly affects markets and their
participants.
Representative short

term load forecasting method
Regressions
Similar day methods
Neural networks
Similar Day

Based Wavelet Neural
Networks
Similar day

based wavelet neural network
method (SIWNN) is developed to predict
tomorrow’s load.
Consists of
similar

day based input selection
,
wavelet decomposition
, and
neural networks.
Similar Day

Based Wavelet Neural
Networks
Main idea is to select the similar day’s load as the
input load, apply wavelet to decompose it into low
and high frequency components, and then use
separate networks to predict the two components
of tomorrow’s load.
Similar Day

Based Wavelet Neural
Networks
Load affecting factors
Weekday Index
Weather
Similar Day

Based Load Input Selection
Decomposition Input Load
Neural Networks
Weekday Index
Weekday index is an important load affecting
factor in view that different days of a week
generally have different load shapes
Weather

winter
Weather information used in SIWNN includes wind

chill
temperature, humidex, wind speed, cloud cover, and
precipitation.
Temperature that is felt could be much lower than air
temperature in winter cause of wind, so
wind

chill
temperature
is used for winter.
T
wc
:wind

chill temperature
T
a
:air
temperature
v
:wind speed
Weather

winter
Scatter plot of load versus
T
wc
Convert to a near linear pattern by processing with
the V

shaping function:
Weather

summer
The combined effects of heat and humidity cause
high level of discomfort in summer. Therefore,
humidex
that measures the combined effect of
heat and humidity is used for summer
H
:humidex
T
a
:air
temperature
D
:dew point
Weather

summer
Also Convert to a near linear pattern by V

shaping
function:
Similar Day

Based Load Input
Selection
Historical load is usually used as input for neural
network based prediction.
Common practice is to use the most recently
available load, like the load of yesterday, and the
load of one week ago with the same weekday index.
Similar Day

Based Load Input
Selection
Similar day selected is required to have the same
weekday index and similar weather to that of
tomorrow, and also required to have its day

of

a

year index within a neighborhood of that of
tomorrow to avoid seasonal variations.
f
:tomorrow (
the forecasted
day)
i
:historical day
w :
weather factor
(wind

chill in winter, humidex in summer)
Similar Day

Based Load Input
Selection
Scatter plot and correlation coefficient of common
and proposed methods
Correlation coefficient
= 0.67
Correlation coefficient
= 0.95
Common (versus yesterday)
Proposed (versus similar day)
Decomposition Input Load
Daubechies wavelets are good for load forecasting
since they are orthogonal wavelets, and will not
cause information loss in the frequency domain.
In SIWNN, Daubechies 4 wavelet (Db4) is used to
decompose the input load into a low frequency
component and a high frequency component.
Decomposition Input Load
L is the scaling function for Db4 used to filter out high
frequency component from the selected similar day’s load.
Down

sampling: Reduce data volume by dropping odd
indexed data points
Up

sampling: Pad zeros to the down

sampled data so as to
recover data length
Low

pass filter: Remove distortion caused by up

sampling.
Decomposition Input Load
Wavelet decomposition result for New
England,2006
Zoom in the original and low frequency for some
hours
Neural Networks
Two three

layer perceptron networks are
separately used for the low frequency component
and the high frequency component.
Inputs are selected based on testing experience.
Neural Networks
The two networks are first trained by using historical actual
data, with the similar day

based selection criteria applied to
each day in the training period.
Training process terminates when the training error is less
than a specified threshold. To avoid over

fitting, for each
network, number of hidden neurons, input selection, and
threshold value for terminating training are determined
based on extensive testing.
Predictions generated by the
two networks are added up to
be tomorrow’s forecasted load
.
Testing results
Three examples are presented below.
Example 1: Uses a classroom

type problem to
examine the value of using wavelet decomposition.
Example 2: Predicts New England 2006 load,
demonstrates the values of wind

chill temperature,
humidex, and weather preprocessing, and examines
sensitivity of prediction to weather forecasting errors.
Example 3: Predicts New England 2007 load, and
examines the effects of using wavelet
decomposition, similar day’s load, and
supplemental load on prediction accuracy
Example 1
Consider a signal:
Five hundred noisy data set were
randomly generated for training
Object is to find
y(t),
t=501~520
Example 1
Our method SIWNN and the standard NN method
that uses a single neural network without wavelet
decomposition are tested.
MAE is 0.86 for SIWNN, and 2.89 for the standard
NN method
Example 2
–
Case 1
This example predicts New England 2006 load,
and includes four cases.
Case 1: Compares using wind

chill temperature
versus using air temperature
Example 2
–
Case 2
Case 2: Compares using humidex versus using dew
point
Example 2
–
Case 3
Case 3: SIWNN is used to with and without data
preprocessing(v

shaping wind

chill temperature and
humidex)
Effects of the preprocessing on neural network training
speed are also examined by comparing the training iteration
numbers(low, high) frequency
With processing (700, 1230) iterations
Without processing (1540, 3127) iterations
Example 2
–
Case 4
Case 4: SIWNN and the standard NN method are
both tested by using actual weather and predicted
weather. SIWNN is
less sensitive to weather
forecasting errors
as compared with the standard
NN method.
Example 3
–
Case 1
This example predicts New England 2007 load, and
includes four cases.
Case 1: SIWNN and a single network without
wavelet decomposition are compared.
Example 3
–
Case 2
Case 2: Prediction of
high frequency load
is
examined with accuracy measured by MAE
Example 3
–
Case 2
To examine the value of precipitation, the high
frequency network is tested with and without
precipitation.
Example 3
–
Case 3
Case 3: Compares using the similar day’s load
versus the standard practice of using the most
recent load
Example 3
–
Case 4
Case 4: SIWNN is used with and without the
supplemental load(today’s predicted load) to
examine its value.
Conclusion
This paper presents a framework that combines similar day
selection, wavelet decomposition, and neural networks to
forecast tomorrow’s load.
Key idea is to use similar day’s load supplemented by
today’s predicted load as input load, and use a synergistic
combination of wavelet decomposition and neural networks
to capture key features of load at low and high frequencies
This method has been extended for holiday load forecasting,
and very short

term load forecasting.
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